Question

If one were to apply Bohr model to a particle of mass ${}^{\prime }{m}^{\prime }$ and charge ${}^{\prime }{q}^{\prime }$ moving in a plane under the influence of a magnetic field $B$, the energy of the charged particle in the $n^{th}$ level will be:

• A. n$\left(\frac{hqB}{8\pi m}\right)$
• B. n$\left(\frac{hqB}{4\pi m}\right)$
• C. n$\left(\frac{hqB}{2\pi m}\right)$
• D. n$\left(\frac{hqB}{\pi m}\right)$

Answer 1

Answer: (B)

n$\left(\frac{hqB}{4\pi m}\right)$

We know that,

$mvR=\frac{nh}{2\pi }$

$R=\frac{nh}{2\pi mv}.............\left(1\right)$

Also we know that

$qvB=\frac{m{v}^2}{R}.........\left[centripetalforce\right]$

$qBR=mv$

$qB\left(\frac{nh}{2\pi mv}\right)=mv$

$\frac{1}{2}n\left(\frac{qBh}{\pi m}\right)=m{v}^2$

$\frac{1}{4}\left(\frac{nhqB}{\pi m}\right)=\frac{1}{2}m{v}^2$

$E=n\left(\frac{hqB}{4\pi m}\right).$

Hence, this is the required solution.